Hidden String Order in a Hole Superconductor with Extended Correlated Hopping.

Ultracold fermions in one-dimensional, spin-dependent nonoverlapping optical lattices are described by a nonstandard Hubbard model with next-nearest-neighbor correlated hopping. In the limit of a kinetically constraining value of the correlated hopping equal to the normal hopping, we map the invariant subspaces of the Hamiltonian exactly to free spinless fermion chains of varying lengths. As a result, the system exactly manifests spin-charge separation and we obtain the system properties for arbitrary filling: ground state collective order characterized by a spin gap, which can be ascribed to an unconventional critical hole superconductor associated with finite long range nonlocal string order.

Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice.

Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field.

Non-standard Hubbard models in optical lattices: a review.

Originally, the Hubbard model was derived for describing the behavior of strongly correlated electrons in solids. However, for over a decade now, variations of it have also routinely been implemented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the vast literature on this subject, with a focus on more recent non-standard forms of the Hubbard model.

Tunneling-induced restoration of the degeneracy and the time-reversal symmetry breaking in optical lattices.

We study the ground-state properties of bosons loaded into the p band of a one-dimensional optical lattice. We show that the phase diagram of the system is substantially affected by the anharmonicity of the lattice potential. In particular, for a certain range of tunneling strength, the full many-body ground state of the system becomes degenerate.

Dipolar molecules in optical lattices.

We study the extended Bose-Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling terms. Using exact diagonalization and the multiscale entanglement renormalization ansatz, we show that these terms can destroy insulating phases and lead to novel quantum phases. These considerable changes of the phase diagram have to be taken into account in upcoming experiments with dipolar molecules.